What's an appropriate buy-in for satellites to a bigger tournament? Let's do some reasoning around this.

The risk of not qualifying

Sure, you may win the satellite and enter the target tournament on the cheap. (Although this is not entirely true, as we'll see below.)

This is what we all hope for, and it's probably what drives hordes of players to the WSOP satellites every spring.

But you may also fail and leave the satellite empty handed. In fact, you could be playing an unlimited number of satellites and still not win a seat.

Alen Cunningham in the WSOP

The worst case scenario is when you pay as much for satellites as you would for the target tournament itself, but without qualifying.

Of course it would be silly to invest that much in satellites. But the question is, how many satellites will you play before you give up? And what will you do if you fail - buy in anyway or skip the tournament?
Expected total buy-in

If you're an average player, the average amount of satellite buy-ins you will have to pay before qualifying equals the target tournament buy-in.

If the target tournament is $100, you'll be playing on average ten $10 satellites before qualifying.

The meaning of this is that the expected cost for entering in the target tournament remains unchanged whether you play satellites or buy in directly. On average, a $100 tournament will cost you $100 to play regardless.

So, for average players, satellites don't change their expectation, they just increase the variance. Instead of paying $100 every time, you will pay sometimes $10, sometimes $200 (unless you quit, in which case you pay something for nothing).

Add to this that each satellite has a fee attached to it, so on average you're actually paying more for the target tournament than if you bought in directly.

Plus, satellites takes time, wich also rpresents an alternative cost (if you have a job).

With that said, what kind of buy-in seems reasonable for a satellite?
Sound limits for satellite buy-ins

Taking the above into consideration, for most players, playing $3 satellites to $1,000 tournaments is kind of pointless. The expected buy-in is still $1000, and the chances of qualifying are slim.

What usually happens is that you don't get to play the tournament. I'm sure you recognize that pattern.

On the other hand, if the satellite buy-in corresponds to 10 or 20 percent of the target tournament buy-in, then you have a real chance of qualifying.

If you do qualify, you play the tournament on the cheap (in a sense). If you don't qualify, you can still buy in to the target tournament and your total buy-in isn't that much higher than it would've been anyway.

In my view, these are sound levels for satellite buy-ins in relation to the target tournament buy-in.

The next question is, what's a reasonable price level for target tournaments? How high should you aim? Let's do some more reasoning.
How big tournaments to satellite for

If you won $10,000 in cash games or a lottery, would you buy in to the WSOP Main Event?

If not, you probably shouldn't play satellites to the WSOP Main Event either.

It's easy to think that if you win a satellite, you get to play the bigger tournament for free. But this is faulty thinking. You're still paying full price for the tournament.

You're paying with the money you won in the satellite.

If this sounds weird, here's why: Defeating 100 players in a $10 satellite and winning a $1,000 tournament buy-in is no different in theory than defeating 100 players in a $10 freezeout and winning $1,000 in cash.

Except that if you win a satellite you're not free to spend the money the way you like. You have to use it for the buy-in.

When you win a satellite, you actually win an amount equal to the target tournament buy-in. You just don't get to see the money.
Conclusion

My conclusion is, if you don't want to spend the money on a tournament buy-in, don't play in the satellites. For if you win, you must pay up.

If you stick to my recommendation for satellite buy-ins above (10% to 20% of the target tournament buy-in or so), this will come naturally. I mean, if you're not ready to cough up $10,000 to play in the WSOP Main Event, you probably won't pay $2,000 for a satellite either.

For sure, there's nothing wrong in taking a shot at a big one. That's not what I'm saying. It's exciting, and good things can come out of it.

Just remember that you're out of your comfort zone and playing over your bankroll. In a sense, it's money wasted. Or at least, it's a gamble.